Abstract

This paper introduces a hierarchical, decentralized,
and parallelizable method for dealing with optimization
problems with many agents. It is theoretically based on a hierarchical
optimization theorem that establishes the equivalence
of two forms of the problem, and this idea is implemented using
DMOC (Discrete Mechanics and Optimal Control). The result
is a method that is scalable to certain optimization problems
for large numbers of agents, whereas the usual “monolithic”
approach can only deal with systems with a rather small
number of degrees of freedom. The method is illustrated with
the example of deployment of spacecraft, motivated by the
Darwin (ESA) and Terrestrial Planet Finder (NASA) missions.